# GeoGebra

## Simple Harmonic Motion perspectives

This is a common example used in the JC1 topics of Oscillations, where if one were to look at an object moving in circles from the side view, it will appear to move in simple harmonic motion. This simple 3D animation allows users to rotate the view to see exactly that. Right click and drag to rotate the view. If you are using a mobile device, use two fingers to drag.

To access the animation in full screen, visit https://www.geogebra.org/m/tsz95u6p

## Displacement-time graph with animation

This displacement-time graph is used in conjunction with an SLS package to help students learn how to describe motion of an object and to use gradient of a tangent to calculate the magnitude of velocity.

For a direct link to the app, go to https://www.geogebra.org/m/k3ja7bnm

I added a little spider to help students visualise the movement with time.

I made some refinement to an applet created last year to demonstrate how vector addition can be done either using vector triangle or parallelogram methods.

To access directly in Geogebra, the link is https://www.geogebra.org/m/p2yvdsvs

## Unit Conversion Self-Practice

This new applet is designed for students to practise conversion of common units used in physics on their own. There is a checking algorithm within, which might need some fine-tuning. For full screen view, click here.

The worked solutions given will demonstrate the breakdown of steps that could help students learn the procedure to convert these units.

## Standard Form and Prefixes

This little applet is designed to allow students to change the order of magnitude and to use any common prefix to observe how the physical quantities are being written. To view this applet in a new tab, click here.

Standard form (also known as scientific notation) is a way of writing very large or very small numbers that allows for easy comparison of their magnitude by using the powers of ten. Any number that can be expressed as a number, between 1 and 10, multiplied by a power of 10, is said to be in standard form.

For instance, the speed of light in vacuum can be written as 3.00 × 108 m s–1 in standard form.

When a prefix is added to a unit, the unit is multiplied by a numerical value represented by the prefix. e.g.     distance = 180 cm = 180 x 10-2 m = 1.80 m

The purpose of using prefixes is to reduce the number of digits used in the expression of values. Hence, students can use the prefix slider to find a user-friendly expression, such as 682 nm instead of 0.000000682 m.

The ten prefixes used are:

## Appreciating the least square method of determining best-fit line

This interactive is designed to help students understand the statistical approach underpinning the drawing of a best-fit line for practical work. For context, our national exams have a practical component where students will need to plot their data, often following a linear trend, on graph paper and to draw a best-fit line to determine the gradient and y-intercept.

The instructions to students on how to draw the best-fit line is often procedural without helping students understand the principles behind it. For instance, students are often told to minimise and balance the separation of plots from the best-fit line. However, if there are one or two points that are further from the rest from the best-fit line (but not quite anomalous points that need to be disregarded), students would often neglect that point in an attempt to bring the best fit line as close to the remaining points as possible. This results in a drastic increase in the variance as the differences are squared in order to calculate the “the smallest sum of squares of errors”.

This applet allows students to visualise the changes in the squares, along with the numerical representation of the sum of squares in order to practise “drawing” the best-fit line using a pair of movable dots. A check on how well they have “drawn” the line can be through a comparison with the actual one.

Students can also rearrange the 6 data points to fit any distribution that they have seen before, or teachers can copy and modify the applet in order to provide multiple examples of distribution of points.